People play games to have fun, right? And part of that is making jokes. But from what I've seen, most people don't seem to take comedy gaming seriously. It sounds funny, but it's true.
They seem to get comedy gaming confused with what I am calling "joke gaming." The big difference is that comedy gaming takes at least some part of itself seriously, be it the setting, the characters or the plot. Without taking some aspect seriously, the game is going to devolve into a series of bad punchlines and an unplayable plot.
Paranoia, although a lot of fun, is definitely a joke game. The setting is George Orwell's 1984 as an amusement park (where everything is wonderful OR ELSE!), the characters have no guarantee that they will be competent in their assigned task (though they generally are competent at something), and the plot is crazily convoluted (all of the characters are secretly traitors to the Computer and are often assigned missions by their traitorous friends to complete alongside the mission given to them by the all-seeing Computer, all while trying to score points with the Computer by turning in any traitors they discover).
Here are a few comedies I've seen and how they fit into the breakdown of Setting, Plot and Characters.
Red Dwarf: The setting and plots were actually rather serious science-fiction fare. What really made it funny were the characters (Dave Lister is the last man in the universe you'd pick to be the Last Man in the Universe).
Discworld: The only thing that got taken seriously in any consistent way was the plot. There are serious characters (Commander Vimes) and not-so serious characters (Captain Carrot). The setting is home to places like Bad Ass and the Place Where The Sun Does Not Shine. When Ankh-Morpork was ruled by a dragon in Guards! Guards! a few members of the City Watch tried to slay the dragon by making the odds against themselves 1,000,000:1 (because million to one chances turn up nine times out of ten). But the plots themselves are rather serious. Rincewind saves the Disc on numerous occasions, Vimes solves murders, and so on.
Hitchhikers Guide to the Galaxy: Here we come full circle. In the Hitchhiker's Trilogy (all 5 volumes!), it seems like the characters are the only serious element. The setting is (maybe) science-fictionally probable, but contains such ludicrous artifacts as the Infinite Improbability Drive, the Vogons, and God's Last Message To His Creation (We Apologize For The Inconvenience). The plots are more picaresque than anything, as the characters bounce around from one ridiculous planet to another. Douglas Adams is quite good at highlighting the silliness of his universe by having at least one character (typically Arthur Dent) notice it and comment on it.
It looks like all my examples are British, which may say something about my sense of humor, or just the fact that I haven't been exposed to the great American humorists (are there any?).
In an RPG scenario, it's oddly difficult to do a character based comedy. Since most players expect to be the heroes of their adventures, they will often be highly resistant to being the butt of very many jokes. Even the Red Dwarf RPG (yes, it exists and I own it) ascribes the typical character with a basic level of competence, even though the main joke of the series is the incompetence of the characters.
If a plot isn't interesting and at least somewhat serious, players will be very unlikely to go along with it. So most of the humor of comedy gaming will typically come from setting.
Another thing to be wary of in comedy gaming is punchlines. For starters, since the player-characters have free will, getting them to go along with a specific plan of action takes some doing. For another, you're basically setting up only one joke. This runs the risk of the players not appreciating your joke. If you plan for a number of small jokes, one-liners and such, the chance that the whole experience will be marred by one bad joke diminishes significantly. Also, by using multiple jokes, it allows you to "read the room" to see which jokes are appreciated and which ones aren't, allowing you to tailor the comedy experience.